Emulation

Accelerate Programme

• Computer Lab hosts Accelerate Programme for Scientific Discovery
• Use ML techniques to deliver scientific advances
• Four DECAF fellows: MPhil Projects Available!

Related Approaches

• Probabilistic Programming
• Approximate Bayesian Computation
• Causal inference

Probabilistic Programming

• Dates back to BUGS
• Modern descendent (same spirit) is Stan
• Also languages like pyro (based on PyTorch)

Approximate Bayesian Computation

Causality

Emulation

Deep Thought and the Challenge of Computation

• Deep Thought computed for 7.5 million years
• Answer: “42”
• Problem: Didn’t know the question
• Built Earth as a computer to find the question
• Illustrates challenges with complex computations

When you are a Bear of Very Little Brain, and you Think of Things, you find sometimes that a Thing which seemed very Thingish inside you is quite different when it gets out into the open and has other people looking at it.

A.A. Milne as Winnie-the-Pooh in The House at Pooh Corner, 1928

Surrogate Modelling in Practice

• Emergent phenomena require computational power.
• In surrogate modelling we use statistical/ML models to learn regularities in those emergent phenomena.

Types of Simulations

• Three main categories:
  • Differential equation models
  • Discrete event simulations
  • Software system simulations

Differential Equation Models

• Two main approaches:
  • Abstracted (e.g., epidemiological models)
  • Fine-grained (e.g., climate/weather models)
• Based on mathematical representations
• Often require numerical solutions

Discrete Event Simulations

• Two main types:
  • Turn-based (Game of Life, F1 Strategy)
  • Event-driven (Gillespie algorithm)
• Updates happen at specific moments
• Can be regular or irregular intervals

Software System Simulations

• Used for testing production code
• Enable “what if” scenarios (counterfactuals)
• Can involve entire codebases
• Useful for complex interacting systems

F1 and Fidelity

• Simulations work at different fidelities
  • F1 Race Strategy vs Aerodynamics
• Must maintain consistent granularity
• Adding detail can degrade performance

Epidemiology

Modelling Herd Immunity

\[ \frac{\text{d}{S}}{\text{d}t} = - \beta S (I_1 + I_2). \]

\[ \frac{\text{d}{E_1}}{\text{d}t} = \beta S (I_1 + I_2) - \sigma E_1. \]

\[ \frac{\text{d}{E_2}}{\text{d}t} = \sigma E_1 - \sigma E_2. \]

\[ \frac{\text{d}{I_1}}{\text{d}t} = \sigma E_2 - \gamma I_1, \]

\[ \frac{\text{d}{I_2}}{\text{d}t} = \gamma I_1 - \gamma I_2. \]

\[ \frac{\text{d}R}{\text{d}t} = \gamma I_2. \]

Strategies for Simulation

• Split variables into state variables, parameters and results.
• In herd immunity
  • State variables: susceptible, exposed, infectious, recovered.
  • Parameters: reproduction number, expected lengths of infection, lockdown timings.
  • Results: e.g. total number of deaths

Strategies for Simulation

• Use emulator to map from e.g. parameters to total number of deaths.
• Treat parameters and results of simulator as inputs and outputs for emulator.

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Backtesting Production Code

• Third major type of simulation
• Running system code counterfactually
• Examples include:
  • Supply chain systems
  • Autonomous systems (Prime Air)
  • Voice assistants (Alexa)
  • Automated buying systems
• Challenges:
  • Intellectual debt
  • ML component interactions
  • System complexity

Alexa

Alexa

Alexa

Speech to Text

Cloud Service: Knowledge Base

Text to Speech

Prime Air

Supply Chain Optimization

Supply Chain Optimization

Forecasting

Inventory and Buying

• Automated buying based on:
  • Supplier lead times.
  • Demand Forecast.
  • Cost basis of the product.

Buying System

Monolithic System

Service Oriented Architecture

Intellectual Debt

Examples in Python

• Wide range of Python simulation tools:

  • SimPy - Discrete event simulation
  • OpenAI Gym - Control problems
  • Fluid dynamics and FEA examples
  • Domain-specific examples (F1, supply chain)

• Simpy

• News Vendor Problem in python (for ordering NFL Replica Jerseys.

• Amazon Supply Chain

• Trolley & Pendulum using sympy (symbolic python)

Examples in Python

• Mountain Car in the OpenAI Gym.

• Hodgkin Huxley by Mark Kramer.

• Formula One Race Simulation in Python by Nick Roth.

• Fluid Dynamics Discretisation of PDEs

• Stress in a connecting rod Discretisation of PDEs

• Network simulation Discrete Event simulation.

• Gillespie Algorithm notebook (in Python 2.7).

Conclusions

• Characterised types of simulation.
  • Physical laws
  • Discrete event
  • Production Software Systems
• Introduced notion of emulation to replace simulation.
• Overviewed GPy software.